+1 for seemingly missed answer, even has been appropriately updated for Episode 6.
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turboJan 29 '13 at 14:38

When this question was a little more current back around EP 3 I think Agent86's answer was the best. Now that some time has past and you've gone to the effort of keeping it current through EP 6 I'll pass it on to you. In truth I kind of lost interest in H4 when they had the big delay in Dec/January to continue releasing Spartan Ops episodes. Thanks for keeping up with this!
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HotinRhinoMar 8 '13 at 1:45

We can probably limit our search somewhat, since there are some "obviously better" spots to farm. Here's my hit list of best Spartan Ops (only the first 3 episodes have been released, so this might need updating later...) For the purposes of this, I've played the op on Normal, solo, and killed any allied units that might steal kills. There may be some variance in the enemy types depending on the difficulty, but the time invested in playing Heroic/Legendary vs the XP/kills is probably not worth it.

Prometheans

For Prometheans, the "overall best" is currently E2C5 (Gagarin). On this op, there are:

40 Crawlers

3 Crawler Snipers

55 Crawler Primes

16 Knights

3 Knight Battlewagons

1 Knight Commander

8 Watchers

This one is made easier by the fact that there are incineration cannons on a rack on the second story of the central area. There's also a lot of shotguns and shotgun ammo, which on Normal will kill a Knight pretty quickly.

I believe there are more Watchers on E2C1 (Cleanup), but it takes a while to get to them so I wouldn't suggest farming Watchers here unless you've also got some Covenant enemies to farm.

Covenant

For Covenant, there are a couple of good ones. The one that I prefer to run is E3C4 (Shootout In Valhalla, aka "the Mantis one"), which has:

27 Grunts

17 Grunt Imperials

0 Grunt Ultras

24 Jackals

4 Jackal Majors

11 Jackal Rangers

32 Elites

0 Elite Zealots

19 Elite Officers

2 Elite Generals

12 Hunters

0 Ghosts

26 Banshees

1 Wraith

Halfway through, you'll gain a Mantis, and it will respawn if it is destroyed, as many times as you need it. Killing a Banshee also gives you credit for an elite, and they're pretty easy to down in a Mantis.

If you want some Grunt Ultras in your Spartan Ops, you might try E3C1 (The VIP, aka "the Scorpion one"):

28 Grunts

24 Grunt Imperials

7 Grunt Ultras

1 Jackal

5 Jackal Majors

25 Jackal Rangers

20 Elites

1 Elite Zealot

12 Elite Officers

7 Elite Generals

0 Hunters

0 Ghosts

0 Banshees

4 Wraith

About halfway through this level, you'll get another vehicle (TANK!) that respawns if it is destroyed. It's pretty easy to lay waste to everything with the tank. Even the early part is pretty easy, as after the first wave you'll get a drop of power weapons that make taking the hill fairly trivial.

We're still kind of low on Elite Zealots and Jackal Majors, so consider E3C5:

31 Grunts

19 Grunt Imperials

7 Grunt Ultras

13 Jackals

17 Jackal Majors

29 Jackal Rangers

3 Elites

14 Elite Zealots

1 Elite Officer

2 Elite Generals

2 Hunters

0 Ghosts

0 Banshees

0 Wraiths

NOTE: Playing this on normal significantly increases grunt ultras. There will be at least 11 before the second phase of the mission. So bear in mind if you are finished with the others and want to focus on ultras.

This one goes a lot slower, as there's not an abundance of vehicles or power weapons. I'd almost consider waiting it out for another Op that is somewhat easier and contains the enemies you need.

Other Notes

There's not a lot of Ghosts in my suggested hit list. There are some on E1C1 (Land Grab, includes multiple empty wraiths, ghosts, and one of each warthog), although there's a lot of dead space in that one and farming them solo's not great. Beyond that, killing Ghosts in War Games also counts towards this commendation, so you could also get progress by playing something like Big Team Slayer.

If I've got to farm just Hunters or Ghosts (ie, for a challenge), I'd probably go for E2C3 (Hacksaw). You can grab a rocket launcher at the beginning by sprinting straight ahead, and then there is more ammo at every location where the marines are under fire. Around the ramp up to the central structure are always 2 Hunters and 1 Ghost.

As a side note, if you're farming a particular type of enemy, you can kill that enemy and then restart the op and still get commendation/challenge credit for the kill.

Conclusion

While I understand you may want to farm commendations for the OCD value, the XP bonuses are very limited compared to the pain involved. I will tend to do the weekly challenges, but I don't give much time to worrying about the commendations, personally.

If you're just in it for XP, solo'ing will give you a better shot at getting a kill yourself, but you'll gain far more XP (2x or more!) by playing in a matchmade game.

Farming Hunters on E2C4 would probably be better than C3 (AKA "The Mantis One") Doing that solo was interesting, especially with the drop pod with 6 hunters in it landed...
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tombull89Nov 28 '12 at 14:46

@tombull89, for just Hunters, I suggest(ed) E2C3 - you can play on Easy, murder a couple of hunters with the rocket launcher, then restart the chapter and go kill them again. If you're farming more Covenant types I still think E2C3 is superior, even in solo. If you're getting pinned down in the Mantis, try getting further away and letting them trickle towards you. My kills per unit time are quite a bit better with a vehicle, though YMMV.
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agent86Nov 28 '12 at 15:40

I'll keep a watch on this as more missions become avail, but I suspect agent86 or others will similarly edit to keep it current. In terms of the Hunter debate, Agent is correct for pure farming E2C3 works out faster, but I can't take the monotony of constant reloading. I mean, farming is bad enough, but at least the game can buy me dinner first (i.e. give me a huge robot to mow down my enemies with).
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HotinRhinoNov 29 '12 at 1:26

Chapter 4 of episode 3 (Shootout in Valhalla) is the best place for Hunter farming.
Grab a Mantis, and there are 10+ even on easy.
Takes about 10 minutes for the whole mission on solo, plus gives TONS of Banshee kills.

The number of Watcher kills required to reach the next rank in commendation is ridiculous given that the most any mission has is about 15-20. Therefore, I found an easier way to farm them.

I think it's the 2nd chapter of Episode two (You start off in the Ragnarok map), create a loadout with the firepower and ammo perks, pick two precision rifles (I prefer the DMR and Light Rifle) and snipe the watcher flying around at the far base. Remember, Knights release Watchers if they are unaware of your presence. You'll get roughly 30 Watcher kills in, say, 5-6 minutes.

Welcome to Arqade! We're a Q&A site, not a discussion forum, so I edited your answer a bit to focus on the problem the asker is facing. You can take a look at the About page for more info.
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BrantJan 29 '13 at 5:23